The global-in-time existence of bounded weak solutions to a large class of physically
relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure is …

Research on spatially extended excitable systems with cross-diffusion components is
reviewed. Particular attention is given to the new phenomena of the quasi-soliton and half …

The global existence of non-negative weak solutions to a strongly coupled parabolic system
arising in population dynamics is shown. The cross-diffusion terms are allowed to be …

The aim of this paper is to investigate the mathematical properties of a continuum model for
diffusion of multiple species incorporating size exclusion effects. The system for two species …

This paper deals with a micro–macro derivation of a variety of cross-diffusion models for a
large system of active particles. Some of the models at the macroscopic scale can be viewed …

In this work we investigate the process of pattern formation in a two dimensional domain for
a reaction–diffusion system with nonlinear diffusion terms and the competitive Lotka …

In bounded n-dimensional domains Ω, the Neumann problem for the parabolic equation
ut=∇⋅(A (x, t)⋅∇ u)+∇⋅(b (x, t) u)− f (x, t, u)+ g (x, t)(*) is considered for sufficiently regular …

This work is concerned with a two-component parabolic system accounting for a doubly
cross-diffusive interaction mechanism which was predicted in Tsyganov et al.(2003)[48] as …

In this work we investigate the phenomena of pattern formation and wave propagation for a
reaction–diffusion system with nonlinear diffusion. We show how cross-diffusion destabilizes …

The mathematical modelling and simulation of ion transport through biological and synthetic
channels (nanopores) is a challenging problem, with direct application in biophysics …